i reckon so, people can say well if you train karate full contact with proper sparring and ****, well whatever whens the last time you saw a karate dojo that didnt have everyone just parroting techniques with compliant partners and breaking flimsy boards.
i've seen black belts that a person with no training can whip.
but in most cases 6 months is nothing,i don't think that a good trainer will have you on the heavy bag yet,you will still be doing footwork drills
There's no such thing as an average Karate Black Belt because of the number of different styles. Some focus on Kata, some focus on sport and some focus on self-defence.
There's also no such thing as an average boxer with 6+ months of training either. Why, because everyone is built differently.
Your question is too open to interpretation. However, if I was going to pick an easy fight, I'd take the boxer, having been trained in Ju-Jitsu and numerous other arts including Boxing for over 23 years. Why pick the boxer to fight? Too predictable and unlike the Boxer, I don't have rules at the back of my mind.
I think it depends on how they practice Karate. In the Olympics, Karate is basically scored on a hit per hit basis. You make one good hit, the action is stopped and you are awarded a point. This doesn't simulate real fights very well. But then there is also full contact karate, which can be considered something like Kickboxing. This would be a boxer's match in a full-contact match.